Hello Swellben,
We understand that you're not able to receive emails with your @mac address. With that being said, we'd like to provide you with a few steps that may help resolve this issue so that you can reset your Twitter password:
"Things to check first
- Check the system status of iCloud Mail.
- Check that you turned on iCloud Mail:
- On your Mac, open the Mail app then choose Mail >Preferences. Click Accounts, then select your iCloud account in the sidebar. Under Account Information, make sure that the account is turned on and the status is online.
3. Make sure you that haven't exceeded your iCloud storage limit. If you exceed your iCloud storage limit, learn how to make more space available in iCloud.
4. Make sure that you're using the latest version of software on your device.
If you can't receive mail in the Mail app on your Mac
- On the left side of the main Mail window, find the name of your iCloud email account. If your account name is dimmed and has a lightning-bolt symbol next to it, your account is offline.
- To take your account online, connect to the Internet.
- Choose Mailbox. If Take All Accounts Online is dimmed, your accounts are already online."
More details here: If iCloud Mail isn't working
Let us know if this helps.
Take care!